We are given that,

We need to find the value of A + A^T.

We know that the transpose of a matrix is a new matrix whose rows are the columns of the original.

We have,

Here,

1^st row of A = (1 2)

2^nd row of A = (3 4)

Transpose of this matrix A, A^T will be given as

1^st column of A^T = 1^st row of A = (1 2)

2^nd column of A^T = 2^nd row of A = (3 4)

Then,

For addition of two matrices, say X and Y, where

Add the corresponding elements of matrices X and Y.

Similarly, we need to add these two matrices, A and A^T.

Adding the corresponding elements of the matrices A and A^T,

Thus, we get the matrix .